Two particles having mass $M$ and $m$ are moving in a circular path having radius $R$ and $r$. If their time period are same then the ratio of angular velocity will be

The ratio of period of oscillation of the conical pendulum to that of the simple pendulum is : (Assume the strings are of the same length in the two cases and $\theta$ is the angle made by the string with the verticla in case of conical pendulum)

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at $x =+2\,m$, its velocity is $-4 \hat{ j }\, m / s$. The object's velocity $(v)$ and acceleration $(a)$ at $x =-2\,m$ will be

What is uniform circular motion ? By using proper figure, obtain equation of acceleration ${a_c}\, = \,\frac{{{v^2}}}{r}$ for uniform circular motion. Show that its direction is towards centre.

A particle is moving on a circular path of radius $r$ with uniform speed $v$. The magnitude of change in velocity when the particle moves from $P$ to $Q$ is  $(\angle POQ = 40^o)$

Consider a circle of radius $42\  cm$. An insect crawls with uniform speed of $1.3\  cm/s$ along the chord $AB$ then along the circular arc $BCD$ to reach point $D$ and then following cord $DA$ to reach finally $A$. Time spend by the insect to crawl from $A$ to $A$ is closest to    ......... $\sec$